Estimation of an acoustic velocity model for the CROP M12A
seismic line using a gradient-based Full Waveform Inversion
B. Galuzzi, Computer Science Department, University of Milan-Bicocca E.M. Stucchi, Earth Sciences Department, University of Pisa A. Tognarelli, Earth Sciences Department, University of Pisa
Introduction. This work deals with the application of a Full Waveform Inversion (FWI) (Virieux,
et. al. 2009) (Fichtner, 2010) procedure to increase the resolution of an acoustic velocity model re-lated to a part of the M12A CROP marine seismic profile (Scrocca, et al., 2003). The CROP M12A seismic line was acquired during the Italian Deep Crust Project (CROP), aimed at investigating the structure of the deep crust in Italy. In (Tognarelli et al., 2010) the recorded data were re-processed to enhance the visibility and the resolution of the structures at the shallow depth up to 3-4 s two-way travel time. Nowadays, FWI represents an important tool to build a high-resolution velocity model of the subsurface from active seismic data. Such model is obtained as the global minimum of some misfit function, designed to measure the difference between the observed and the modelled data. In general, the misfit function is highly non-linear with the presence of many local minima due to the well-known cycle skipping effect (Pratt, 2008). Therefore, the optimization problem is solved by means of an iterative gradient-based method, starting from a model as close as possible to the global minimum of the objective function. Besides, the application of FWI to real data requires dedicated specific operations aimed at improving the S/N ratio and obtaining observed data that can be reliably reproduced by a modelling algorithm (Galuzzi et al., 2018).
In this work, we present an application of acoustic FWI on a part of CROP M12A seismic profile. Specific processing operations are applied on both predicted and observed data to increase the robust-ness of the inversion procedure, thus improving the reliability of the final model estimation. The predicted data are obtained by solving the 2D acoustic wave equation, whereas in the local optimiza-tion procedure the steepest descent algorithm is employed. The misfit funcoptimiza-tion used is based on the L2 norm difference between the predicted and observed envelopes of the seismograms (Bozdag et al., 2011). As the starting model, we used the model obtained by (Tognarelli et al., 2010) through the Migration Velocity Analysis (MVA) and used for the post-stack depth migration of the data. To val-idate the FWI final model, we check the improvements on the flattening of the events in the common-image-gathers (CIGs) after pre-stack depth migration.
The seismic data. The CROP M12A seismic dataset consists of 1500 marine seismic shots, acquired
Figure 1: (a) Location of the M12A CROP profile. The red arrow represents the part of the profile used for the inversion. (b) An example of shot gather used in the inversion. The red polygon delimits the portion of the seismogram considered in the inversion.
Modelling. The synthetic data are obtained by means of an explicit, 2nd order in time, finite
differ-ence algorithm which is used to solve the 2D acoustic wave equation. The model dimensions are approximately 24.5 km in length and 2 km in depth. The modelling grid is made by 981x80 nodes, with a uniform grid size of dx=25m. The sea-bed is situated between the 3rd and 4th row of the grid. We put absorbing boundary conditions on the lateral and bottom sides of the model and reflecting boundary conditions at the top side to simulate the sea-air interface. The order of approximation of the spatial derivatives is optimized to reduce the numerical dispersion (Galuzzi et al., 2017). The source wavelet is estimated from the sea-bed reflection.
Design of a robust misfit function. Before performing the Full Waveform Inversion, dedicated
pro-cessing operations are applied on both predicted and observed seismograms to reduce the cycle skip-ping effect and, in general, to circumvent the non-linearity of the optimization problem. As shown in previous studies (Galuzzi et al., 2018) (Mazzotti et al., 2017), we make use of a processing sequence that includes a band-pass filtering between 5 Hz and 15 Hz, envelope computation, and trace-by-trace normalization. Finally, we choose the L2 norm difference between the predicted and the observed data, as the misfit function.
Initial model. Due to the non-linearity of the misfit function, the starting model in the FWI procedure
plays an important role. To assure the convergence of a local optimization method, the initial model must be accurate enough to give a good match between the observed and predicted data. To attain this, we make use of the velocity model obtained from MVA. More details on the estimation of the model can be found in (Tognarelli et al., 2010). Figure 2 shows the MVA velocity model used to pre-stack depth migrate (PSDM) the data. The migration results are illustrated in Fig.3a where 6 GIGs evenly spaced along the profile and displayed up to 2 km of depth can be observed. The flattening of the events on the CIGs, obtained after the PSDM, constitutes a good validation test for the reliability of the MVA velocity model. However, many gathers still present a residual move-out that can be reduced using the FWI based on a gradient line-search method.
Inversion procedure and results. As the local optimization method, we use the steepest descent
velocity model obtained by MVA and at the end of the FWI optimization procedure, respectively. The starting model is refined mainly in the upper part just below the sea-bed.
Figure 2: a) Velocity model obtained by the MVA. b) Velocity model obtained at the end of the FWI optimization procedure.
Figure 3a and 3b show a comparison of 6 CIGs positioned along the seismic profile before and after the FWI inversion. A significant improvement of the horizontal alignment of the events at about 1 km of depth can be noted passing from Fig. 3a to Fig. 3b.
Figure 3: CIGs obtained by pre-stack depth migrating the data using (a) the MVA velocity model and (b) the final velocity model obtained at the end of the local optimization procedure.
Conclusion. In this work, we made an acoustic FWI experience on a portion of the CROP M12A
sequence applied to the data reduces the non-linearity of the misfit function and strengthens the reli-ability of the whole procedure against the cycle-skipping phenomenon. Starting from a velocity model obtained by the MVA, we estimated, by means of a gradient-based method, a final model whose improved quality is assessed by a better horizontal alignment of the events in the CIGs.
Acknowledgements. The seismic data processing is carried out using ProMAX of
Halliburton/Land-mark that is gratefully acknowledged.
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